An inhaler of the generic type is described in U.S. Pat. No. 5,429,122. There, the amount of the substance to be delivered is transferred from a lower storage chamber to an upwardly movable dosing chamber. The dosing chamber is in the form of a ring-shaped groove in (or on) a linearly movable rod which is spring-loaded. A mandrel in the closure cap presses the rod into a retracted (lower) position. When the patient removes the cap, the rod is propelled rapidly upward into a ready-to-empty transfer position. The contents of the dosing chamber are advanced into the mouthpiece via a suction air stream created by the patient. A drawback is that the spring-loaded rapid upward propulsion of the rod tends to provide an incorrect dosage of the substance.